Induced emf at a specific time

In summary, the conversation discusses finding the induced EMF at a specific time for a circular coil in a magnetic field. The formula for calculating EMF is mentioned and the incorrect answer of 36.12 V is given. The correct formula is provided and it is noted that a negative voltage is possible. The importance of using the correct units is also emphasized.
  • #1
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Homework Statement

A circular coil with 35 turns of wire and a diameter of 19 cm is placed in a magnetic field given by B(t) = 6 t^2 + 6 t + 2 T where t is time in seconds. The field is perpendicular to the plane of the coil. What is the induced EMF at t = 5 s?

Homework Equations

E=-d(magnetic flux)/dtime

The Attempt at a Solution


I found E to be 36.12 V but that's wrong. I'm not sure what's wrong. I did E=NAB/time.
 
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  • #2
Emf is proportional to negative the derivative or rate of change of the magnetic flux with respect to time. The area is constant, thus
V = -NA*dB/dt.
 
  • #3
I plugged in -36.12 but it's still wrong. Can we have a negative voltage?
 
  • #4
Could you please tell me where I'm wrong? I have a couple of hours left.
 
  • #5
dB/dt = 12t + 6; at t = 5s, dB/dt = 66T/s
N = 35 turns
A = pi*r^2...so your problem might be that you're using the diameter of 19cm instead of the radius; also, be sure that you convert the given units to the proper units, so the radius = d/2 = 9.5cm = .095m.
The emf is V = -NA*dB/dt...and you could have a negative voltage.
 
  • #6
Thank you very much I appreciate it.
 

What is induced emf at a specific time?

Induced emf at a specific time is the electromotive force that is produced in a circuit due to a change in magnetic flux at a certain moment in time.

How is induced emf at a specific time calculated?

The induced emf at a specific time is calculated using Faraday's Law of Electromagnetic Induction, which states that the emf induced in a circuit is equal to the rate of change of magnetic flux through the circuit over time. The formula is given as: E = -N(dΦ/dt), where E is the induced emf, N is the number of turns in the circuit, and dΦ/dt is the rate of change of magnetic flux.

What factors affect the magnitude of induced emf at a specific time?

The magnitude of induced emf at a specific time is affected by the rate of change of magnetic flux, the number of turns in the circuit, and the strength of the magnetic field. Additionally, the resistance of the circuit can also affect the magnitude of induced emf.

What is the direction of induced emf at a specific time?

The direction of induced emf at a specific time is determined by Lenz's Law, which states that the direction of the induced emf is always such that it opposes the change in magnetic flux that caused it. This means that the induced current will flow in a direction that creates a magnetic field that opposes the original change in magnetic flux.

How is induced emf at a specific time used in real-world applications?

Induced emf at a specific time has many practical applications, such as in generators and transformers, where it is used to convert mechanical energy into electrical energy. It is also used in devices like electric motors and induction cooktops. Additionally, it is used in scientific research, such as in experiments with electromagnetic induction and in studying the behavior of magnetic fields.

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